拟线性双曲-抛物奇异摄动问题的O（ε^3）阶渐近展开  

Asymptotic Expansion for Quasi-linear Singular Perturbation Problem of Hyperbolic-Parabolic Partial Differential Equation

作　　者：陈国玉[1] 邱国新[1] 

机构地区：[1]解放军炮兵学院基础部,安徽合肥230001

出　　处：《甘肃科学学报》2008年第1期20-23,共4页Journal of Gansu Sciences

基　　金：解放军炮兵学院青年后备人才基金(20070523)

摘　　要：为讨论一个拟线性双曲—抛物奇异摄动问题的渐近展开问题,首先用能量方法建立稳定不等式,然后利用双重迭代法对原问题进行渐近展开,最后用稳定不O(ε3)逼近式,从而证明了渐近解的一致有效性.A singular perturbation problem of a quasi-linear hyperbolic-parabolic partial differential equa-tion is discussed. In order to discuss the asymptotic expansion of the problem,the energy method is applied to establish the continuous stability inequality and the 3-order asymptotic expansion of the solution to this problem with respect to small parameters. Thus the uniform effectiveness of the asymptotic expansion is proved.

关 键 词：拟线性奇异摄动问题 双曲一抛物偏微分方程 连续稳定不等式 小参数 

分 类 号：O175.1[理学—数学]